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© 2016

Two-Dimensional Systems

From Introduction to State of the Art

Book

Part of the Studies in Systems, Decision and Control book series (SSDC, volume 28)

Table of contents

  1. Front Matter
    Pages i-xxxi
  2. Abdellah Benzaouia, Abdelaziz Hmamed, Fernando Tadeo
    Pages 1-29
  3. Abdellah Benzaouia, Abdelaziz Hmamed, Fernando Tadeo
    Pages 31-58
  4. Abdellah Benzaouia, Abdelaziz Hmamed, Fernando Tadeo
    Pages 59-74
  5. Abdellah Benzaouia, Abdelaziz Hmamed, Fernando Tadeo
    Pages 75-109
  6. Abdellah Benzaouia, Abdelaziz Hmamed, Fernando Tadeo
    Pages 111-144
  7. Abdellah Benzaouia, Abdelaziz Hmamed, Fernando Tadeo
    Pages 145-165
  8. Abdellah Benzaouia, Abdelaziz Hmamed, Fernando Tadeo
    Pages 167-181
  9. Abdellah Benzaouia, Abdelaziz Hmamed, Fernando Tadeo
    Pages 183-221
  10. Abdellah Benzaouia, Abdelaziz Hmamed, Fernando Tadeo
    Pages 223-270
  11. Abdellah Benzaouia, Abdelaziz Hmamed, Fernando Tadeo
    Pages 271-292
  12. Back Matter
    Pages 293-295

About this book

Introduction

A solution permitting the stabilization of 2-dimensional (2-D) continuous-time saturated system under state feedback control is presented in this book. The problems of delay and saturation are treated at the same time. The authors obtain novel results on continuous 2-D systems using the unidirectional Lyapunov function. The control synthesis and the saturation and delay conditions are presented as linear matrix inequalities. Illustrative examples are worked through to show the effectiveness of the approach and many comparisons are made with existing results.

The second half of the book moves on to consider robust stabilization and filtering of 2-D systems with particular consideration being given to 2-D fuzzy systems. Solutions for the filter-design problems are demonstrated by computer simulation. The text builds up to the development of state feedback control for 2-D Takagi–Sugeno systems with stochastic perturbation. Conservatism is reduced by using slack matrices and the coupling between the Lyapunov matrix and the system matrices is broken by using basis-dependent Lyapunov functions. Mean-square asymptotic stability and prescribed H-infinity performance are guaranteed.

Two-Dimensional Systems emphasizes practical approaches to control and filter design under constraints that appear in real problems and uses off-the-shelf software to achieve its results. Researchers interested in control and filter design for multidimensional systems, especially multi-dimensional fuzzy systems, will find this book a useful resource as will graduate students specializing in dynamical sytems.

Keywords

Asymptotic Stability Delayed Continuous Systems Fornasini-Marchesini Models H-infinity Controller Design LMIs Linear Matrix Inequalities Multidimensional Systems Positive Systems Roesser Models Takagi–Sugeno Fuzzy Systems

Authors and affiliations

  1. 1.Department of PhysicsUniversity of Cadi AyyadMarrakechMorocco
  2. 2.Ecole Supérieure de TechnologieUniversity of Sidi Mohammed Ben AbdellahFèsMorocco
  3. 3.Departamento de Ingeniería de Sistemas y AutomáticaUniversity of ValladolidValladolidSpain

About the authors

Abdellah Benzaouia was born in Attaouia (Marrakech) in 1954. He received the degree of Electrical Engineering at the Mohammedia school (Rabat) in 1979 and the Doctorat (PhD) at the University Cadi Ayyad in 1988. He is actually professor at the University of Cadi Ayyad (Marrakech) where he is also head of the laboratory of research LAEPT, CNRST laboratory. His research interests are mainly constrained control, robust control, pole assignment, systems with Markovian jumping parameters, hybrid systems and fuzzy systems. He collaborates with many teams in France, Canada, Spain and Italy.
Abdelaziz Hmamed was born in Sefrou, Morocco, in 1951. He received his Doctorate of State degree in Electrical Engineering from the Faculty of Sciences, Rabat, Morocco, in 1985. Since 1986, he has been with the Department of Physics, Faculty of Sciences, Dhar El Mehraz at Fes, where he is currently a Full Professor. His research interests are delay systems, stability theory, systems with constraints, 2-d systems and applications.
Fernando Tadeo is Professor of the School of Engineering at the University of Valladolid. He graduated from the same university, in Physics in 1992, and in Electronic Engineering in 1994. After completing an M.Sc. in Control Engineering in the University of Bradford, U.K., he went back to Valladolid, where he got his Ph.D. degree. His main interest area is Feedback Systems with Constraints, in particular Positive Systems, collaborating with teams in Morocco, Tunisia, France and Germany. This research is focused on applications in Process Control (Desalination and Electrolyzation Processes) and Renewable Energies (Wind, Solar and Salinity Gradient).

Bibliographic information

  • Book Title Two-Dimensional Systems
  • Book Subtitle From Introduction to State of the Art
  • Authors Abdellah Benzaouia
    Abdelaziz Hmamed
    Fernando Tadeo
  • Series Title Studies in Systems, Decision and Control
  • Series Abbreviated Title Studies in Systems, Decision and Control
  • DOI https://doi.org/10.1007/978-3-319-20116-0
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Engineering Engineering (R0)
  • Hardcover ISBN 978-3-319-20115-3
  • Softcover ISBN 978-3-319-36915-0
  • eBook ISBN 978-3-319-20116-0
  • Series ISSN 2198-4182
  • Series E-ISSN 2198-4190
  • Edition Number 1
  • Number of Pages XXXI, 295
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Control and Systems Theory
    Computational Intelligence
    Artificial Intelligence
    Signal, Image and Speech Processing
  • Buy this book on publisher's site